Operational Amplifiers

Op amps are versatile ICs containing a hundred or so transistors that can
perform a vareity of mathematical functions. For this reason, they are the
building blocks of many signal processing circuits. They have two inputs, an
inverting (-) and noninverting (+). A positive voltage source and negative
voltage source or ground are connected directly to the op amp, although these
are rarely shown on circuit diagrams. There is a single output, which is
almost always connected to the inverting input with a negative feedback loop.

Op Amps have almost infinite gain, high input impedance, and low output
impedance. Because of this, they serve many useful purposes in analog circuits.
Some of these properties are discussed in the context of the following
examples.

All of the example circuits can be analyzed by observing the following
simple rules.

The output does whatever is necessary to make the voltage difference
across the inputs equal to zero.

The inputs draw no current.

The output voltage does not depend on the output current.

Even though there is a lot going on inside the op amp, these rules describe
its "black box" integrated circuit behavior. Ideal op amps are modeled with
infinite gain and infinite impedance - real op amps only approximate these
model properties. Likewise, while our model assumes infinite voltage gain,
the limiting output voltage magnitude is about 1.4V lower than the magnitude
of the supply voltage (this is due to diode drops in the op amp). Some of these
effects should be observable if we apply a square wave input. At the rising
and falling transitions of the square wave the voltage changes infinitely
fast and while they're fast, op amps can't change instantaneously - there
should be a slightly non-vertical slope produced in the output. This can be
measured by the slew rate (with is the change in voltage over the change in
time).

Inverting Amplifier -
This configuration copies an inverted and scaled version of the input signal
to its output. In doing so, the circuit isolates the circuit that produces
the input reference from the circuit that uses the output by virtue of our
op amp's impedance relationships.

Non-Inverting Amplifier -
We can accomplish amplification without inversion if we re-configure the
circuit slightly.

By setting R2 to zero (short circuit) and R1 to
infinity (open circuit to ground), we get a non-inverting, unity gain
amplifier - the unity-gain follower. This is an important use of
operational amplifiers. The high input impedance of the amp draws virtually no
current and so acts as an impedance buffer. One could, for instance, use a
voltage divider to step the voltage used to drive a resistive load down
without worrying about impedance loading the divider. The op amp lets you
track the input voltage without drawing significant current.

Integrating and Differentiating Amplifiers -
By using a capacitance, the op amp can compute the integral and differential
of the input voltage. In the first example, we see that the output voltage
is the integral of the input voltage.

And by switching the capacitor and the resistor, the output voltage is the
derivative of the input voltage with respect to time.

Adder - This circuit produces and output equal to the
negative weighted sum of the respective inputs. One can imagine that with the
right input resistances, we could construct a form of D/A converter with
in which input "bits" are amplified by an amount proportional to their position
in a binary word.

Comparator - This setup is used to determine which input signal is
greater. When the inputs are equal, there is no output. When the inverting
input is greater, the op amp becomes saturated and output voltage is equal to
the positive voltage supply. When the inverting input is greater, the output
voltage is equal to the negative voltage supply. There are TTL comparators
available that would be recommended for this purpose, but the mighty op amp
can do it in a pinch.